Bedingungen für die Zweispiegeligkeit der Automorphismengruppen von Cayleyalgebren. (Conditions for the bireflectionality of the automorphism groups of Cayley algebras)
This paper is based on a paper of \textit{M. Wonenburger} [J. Algebra 12, 441-452 (1969; Zbl 0177.057)] on the automorphism groups of Cayley algebras. Wonenburger showed that every automorphism of a Cayley algebra over a field of characteristic not 2 is the product of at most three involutory automorphisms \((=\) reflections), or, in other words, that the automorphism group of a Cayley algebra is in general trireflectional. She also gave examples of Cayley algebras over special fields whose automorphism groups are bireflectional. The author is now able to improve Wonenburger's results essentially and to derive necessary and sufficient conditions for the bireflectionality of a Cayley algebra over a field of characteristic not 2. These criteria put rather strong conditions on the base field of the Cayley algebra. Thus in many cases it is possible to decide whether the automorphism group of a Cayley algebra over a given field is bireflectional or not. As an application of his results the author reproves the bireflectionality of the automorphism groups of Cayley algebras over real closed fields.
scientific article; zbMATH DE number 4156696